polyvander(x, deg)
Returns the Vandermonde matrix of degree :None:None:`deg` and sample points x. The Vandermonde matrix is defined by
where :None:None:`0 <= i <= deg`. The leading indices of :None:None:`V` index the elements of x and the last index is the power of x.
If :None:None:`c` is a 1-D array of coefficients of length :None:None:`n + 1` and :None:None:`V` is the matrix V = polyvander(x, n)
, then np.dot(V, c)
and polyval(x, c)
are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of polynomials of the same degree and sample points.
Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array.
Degree of the resulting matrix.
The Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1,)
, where the last index is the power of x. The dtype will be the same as the converted x.
Vandermonde matrix of given degree.
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.ma.extras.vander
numpy.polynomial.polynomial.polyfit
numpy.vander
numpy.polynomial.polynomial.polyvander2d
numpy.polynomial.polynomial.polyvander3d
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